/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q46E One of the cornerstones of quant... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q46E (page 137)

One of the cornerstones of quantum mechanics is that bound particles cannot be stationary-even at zero absolute temperature! A "bound" particle is one that is confined in some finite region of space. as is an atom in a solid. There is a nonzero lower limit on the kinetic energy of such a particle. Suppose minimum kinetic energy of width L. Obtain an approximate formula for its minimum kinetic energy.

Short Answer

Expert verified

The minimum kinetic energy formula isK路E.鈮�h28mL2

Step by step solution

01

Uncertainty principle.

That the position and the velocity of an object cannot both be measured exactly, at the same time, even in theory.

螖x鈭�p鈮�h4蟺

螖xuncertainty in position.

螖puncertainty of momentum.

h Planck's constant.

02

Kinetic energy.

螖x螖p=螖x螖(mv)猢�h2

localid="1659187305509" 螖v=h2m螖x

Here 螖x=L

螖v=h2mL

The kinetic energyK.E.=12m(螖v)2

Substitute the value,

localid="1659187247106" 碍.贰.鈮�h28mL2

Therefore, the minimum Kinetic Energy formula of the width is localid="1659187237799" 碍.贰鈮�.h28mL2

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A beam of electrons strikes a crystal at an angle胃with the atomic planes, reflects of many atomic planes below the surface, and then passes into a detector also making angle胃with the atomic planes. (a) If the minimum胃giving constructive interference is.35掳 What is the ratio位/诲, Where is the spacing between atomic planes? (b) At what other angles, if any, would constructive interference occur?

A beam of particles, each of mass m and (nonrelativistic) speed v, strikes a barrier in which there are two narrow slits and beyond which is a bunk of detectors. With slit 1 alone open, 100 particles are detected per second at all detectors. Now slit 2 is also opened. An interference pattern is noted in which the first minimum. 36 particles per second. Occurs at an angle of 30ofrom the initial direction of motion of the beam.

(a) How far apart are the slits?

(b) How many particles would be detected ( at all detectors) per second with slit 2 alone open?

(c) There are multiple answers to part (b). For each, how many particles would be detected at the center detector with both slits open?

According to the energy-time uncertainty principle, the lifetime鈭�lof a state and the uncertainty鈭�Ein its energy are invertible proportional. Hydrogen's red spectral line is the result of an electron making a transition "downward" frum a quantum state whose lifetime is about10-8s.

(a) What inherent uncertainty in the energy of the emitted person does this imply? (Note: Unfortunately. we might use the symbol for the energy difference-i.e., the energy of the photon-but here it means the uncertainly in that energy difference.)

(b) To what range in wavelength s does this correspond? (As noted in Exercise 2.57. the uncertainty principle is one contributor to the broadening of spectral lines.)

(c) Obtain a general formula relating 鈭�位to鈭�t.

To how small a region must an electron be confined for borderline relativistic speeds say0.05to become reasonably likely? On the basis of this, would you expect relativistic effects to be prominent for hydrogen's electron, which has an orbit radius near10-10m? For a lead atom "inner-shell" electron of orbit radius10-12m?

An electron in an atom can "jump down" from a higher energy level to a lower one, then to a lower one still. The energy the atom thus loses at each jump goes to a photon. Typically, an electron might occupy a level for a nanosecond. What uncertainty in the electron's energy does this imply?
See all solutions

Recommended explanations on Physics Textbooks

Kinematics Physics

Read Explanation

Work Energy and Power

Read Explanation

Physical Quantities And Units

Read Explanation

Magnetism

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Circular Motion and Gravitation

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.